In prior work, it was proven that estimating the spatial cross-correlation function between two subarrays is equivalent to multiplying their conventional beamforming (CBF) outputs to obtain the product processor output (PPO). This is equivalent to the spatial periodogram in [1]}. [1]} also derives the expected value of the PPO for any propagating signal and the covariance of spatially white Gaussian noise, but the authors only incorporate uniform windows in each case. Non-uniform windows are essential to prevent the masking of weak signals due to the sidelobes of strong interferers [3]}. In addition, the results in [1]} do not apply to multidimensional arrays.
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